Originally a sponge cake made with added butter incorporated into the batter..

It is known as Genoise in France and Italy and named after the Italian City of Genoa.

In the UK , the term Genoese is usually given to a more heavy, higher fat content product similar to a Madeira Cake.

A light Genoese  is made by whisking the egg and sugar together (aeration) to form a sponge, the flour is then carefully folded in and a small amount of melted butter added. 

Medium Genoese is a semi-sponge usually made by blending (all in method) the ingredients together but relying more on (Chemical Aeration) ie Baking Powder for any lift/volume.

Heavy Genoese Normally a cake like finish which can be made either by the traditional sugar batter method or as for the Medium Genoese, by the blending (all in method). Another way is by using an older method  by using Boiled Genoese method.

High Ratio Modern day, commercial  production tends to favour this method/type of Genoese. It requires special type flours and fats, not usually readily available to the home baker. It contains more liquid and sugar than the normal. This is to prolong its shelf life (does not stale so quick) and is cheaper to make,  therefore more suited for the mass production market.